Some main-sequence stars of spectral type A are observed to have a strong
(300-30000 G), static, large-scale magnetic field, of a chiefly dipolar shape
– the Ap stars' (for example Alioth, the fifth star in the Big Dipper). Following their discovery fifty years ago, it was speculated that these fields a remnants of the star's formation, a fossil’ field. Alternatively, they could
be generated by a dynamo process in the star’s convective core. The dynamo
hypothesis has difficulty explaining high field strengths and the lack of a
correlation with rotation. The weakness of the fossil-field theory has been the
absence of known field configurations stable enough to survive in a star over
its lifetime. We demonstrate here the formation of stable magnetic field
configurations, with properties agreeing with those observed, by evolution from
arbitrary, unstable initial fields. The results are applicable equally to Ap
stars, magnetic white dwarfs and some highly magnetised neutron stars known as
magnetars. This establishes fossil fields as the natural, unifying explanation
for the magnetism of all these stars.

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